IDEAS home Printed from https://ideas.repec.org/p/tul/wpaper/0802.html
   My bibliography  Save this paper

Tests in Censored Models when the Structural Parameters Are Not Identified

Author

Listed:
  • Leandro M. Magnusson

    (Department of Economics, Tulane University)

Abstract

This paper presents tests for the structural parameters of a censored regression model with endogenous explanatory variables. These tests have the correct size even when the identification condition for the structural parameter is invalid. My approach starts from the estimation of the unrestricted parameters, which does not depend on the identification of the structural parameter. Next, I set up the optimal minimum distance objective function, from where I derive the tests. The proposed robust tests are implemented in many statistical software packages since they demand only the Tobit and the ordinary least squares estimation functions. By simulating their power curves, I compare the robust to the Wald and the likelihood ratio tests. A case of the labor supply of married women illustrates the use of the robust tests for the construction of confidence intervals.

Suggested Citation

  • Leandro M. Magnusson, 2008. "Tests in Censored Models when the Structural Parameters Are Not Identified," Working Papers 0802, Tulane University, Department of Economics.
    • Handle: RePEc:tul:wpaper:0802
    as

    Download full text from publisher

    File URL: http://repec.tulane.edu/RePEc/pdf/tul0802.pdf
    File Function: First version, 2008
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richard Blundell & Ian Walker, 1986. "A Life-Cycle Consistent Empirical Model of Family Labour Supply Using Cross-Section Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 539-558.
    2. Powell, James L, 1986. "Symmetrically Trimmed Least Squares Estimation for Tobit Models," Econometrica, Econometric Society, vol. 54(6), pages 1435-1460, November.
    3. Gourieroux, Christian & Monfort, Alain & Renault, Eric & Trognon, Alain, 1987. "Generalised residuals," Journal of Econometrics, Elsevier, vol. 34(1-2), pages 5-32.
    4. Newey, Whitney K., 1987. "Efficient estimation of limited dependent variable models with endogenous explanatory variables," Journal of Econometrics, Elsevier, vol. 36(3), pages 231-250, November.
    5. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
    6. Smith, Richard J & Blundell, Richard W, 1986. "An Exogeneity Test for a Simultaneous Equation Tobit Model with an Application to Labor Supply," Econometrica, Econometric Society, vol. 54(3), pages 679-685, May.
    7. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    8. Richard W. Blundell & Richard J. Smith, 1989. "Estimation in a Class of Simultaneous Equation Limited Dependent Variable Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(1), pages 37-57.
    9. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    10. Lee, Myoung-Jae, 1995. "Semi-parametric Estimation of Simultaneous Equations with Limited Dependent Variables: A Case Study of Female Labour Supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 187-200, April-Jun.
    11. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    12. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
    13. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, vol. 46(5), pages 1211-1215, September.
    14. Amemiya, Takeshi, 1979. "The Estimation of a Simultaneous-Equation Tobit Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 169-181, February.
    15. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leandro M. Magnusson, 2010. "Inference in limited dependent variable models robust to weak identification," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 56-79, October.
    2. Antoine, Bertille & Lavergne, Pascal, 2023. "Identification-robust nonparametric inference in a linear IV model," Journal of Econometrics, Elsevier, vol. 235(1), pages 1-24.
    3. Guggenberger, Patrik & Smith, Richard J., 2008. "Generalized empirical likelihood tests in time series models with potential identification failure," Journal of Econometrics, Elsevier, vol. 142(1), pages 134-161, January.
    4. Frank Kleibergen, 2004. "Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap," Econometric Society 2004 North American Summer Meetings 408, Econometric Society.
    5. Isaiah Andrews & Timothy B. Armstrong, 2017. "Unbiased instrumental variables estimation under known first‐stage sign," Quantitative Economics, Econometric Society, vol. 8(2), pages 479-503, July.
    6. Gomes, Fábio Augusto Reis & Paz, Lourenço S., 2013. "Estimating the elasticity of intertemporal substitution: Is the aggregate financial return free from the weak instrument problem?," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 63-75.
    7. Kleibergen, Frank, 2009. "Tests of risk premia in linear factor models," Journal of Econometrics, Elsevier, vol. 149(2), pages 149-173, April.
    8. Andrews, Donald W.K. & Cheng, Xu, 2014. "Gmm Estimation And Uniform Subvector Inference With Possible Identification Failure," Econometric Theory, Cambridge University Press, vol. 30(2), pages 287-333, April.
    9. Doko Tchatoka, Firmin, 2011. "Testing for partial exogeneity with weak identification," MPRA Paper 39504, University Library of Munich, Germany, revised Mar 2012.
    10. Leandro M. Magnusson & Sophocles Mavroeidis, 2010. "Identification-Robust Minimum Distance Estimation of the New Keynesian Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(2-3), pages 465-481, March.
    11. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    12. Dufour, Jean-Marie & Taamouti, Mohamed, 2007. "Further results on projection-based inference in IV regressions with weak, collinear or missing instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 133-153, July.
    13. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.
    14. Moreira, Humberto & Moreira, Marcelo J., 2019. "Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors," Journal of Econometrics, Elsevier, vol. 213(2), pages 398-433.
    15. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    16. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1192-1228, December.
    17. Frank Kleibergen & Zhaoguo Zhan, 2021. "Double robust inference for continuous updating GMM," Papers 2105.08345, arXiv.org.
    18. Jun, Sung Jae, 2008. "Weak identification robust tests in an instrumental quantile model," Journal of Econometrics, Elsevier, vol. 144(1), pages 118-138, May.
    19. Bolduc, Denis & Khalaf, Lynda & Moyneur, Érick, 2008. "Identification-robust simulation-based inference in joint discrete/continuous models for energy markets," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3148-3161, February.
    20. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.

    More about this item

    Keywords

    endogenous Tobit; weak instruments; minimum distance estimation; female labor supply;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tul:wpaper:0802. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kerui Geng (email available below). General contact details of provider: https://edirc.repec.org/data/detulus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.